If A =  and A adj A = AAT, then 5a +b is equal to from Mathem

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of all real values of x satisfying the equation
left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent is:

  • 3

  • -4

  • 6

  • 6

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2.

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

  • 46th

  • 59th

  • 52nd

  • 52nd

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3.

If the number of terms in the expansion of open parentheses 1 minus 2 over straight x space plus 4 over straight x squared close parentheses to the power of straight n comma straight x not equal to 0 comma is 28, then the sum of the coefficients of all the terms in this expansion is

  • 64

  • 2187

  • 243

  • 243

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4.

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

  • 8/5

  • 4/3

  • 1

  • 1

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5.

If the sum of the first ten terms of the series,

open parentheses 1 3 over 5 close parentheses squared space plus open parentheses 2 2 over 5 close parentheses squared space plus open parentheses 3 1 fifth close parentheses squared space plus space 4 squared space plus space open parentheses 4 4 over 5 close parentheses squared space plus.....is 16/5 m, the m is equal to

  • 102

  • 101

  • 100

  • 100

347 Views

6.

Let straight p space equals space limit as straight x rightwards arrow 0 to the power of plus of left parenthesis 1 plus tan squared square root of straight x right parenthesis to the power of 1 divided by 2 straight x end exponent comma space then log p is equal to 

  • 2

  • 1

  • 1/2

  • 1/2

371 Views

7.

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60o. Then the time taken (in minutes) by him, from B to reach the pillar, is:

  • 6

  • 10

  • 20

  • 20

182 Views

8.

If 
straight f left parenthesis straight x right parenthesis space plus space 2 straight f open parentheses 1 over straight x close parentheses space equals space 3 straight x comma
straight x space not equal to space 0 space and space straight S space equals space open curly brackets straight x space straight epsilon space straight R colon space straight f space left parenthesis straight x right parenthesis space equals space straight f left parenthesis negative straight x right parenthesis close curly brackets semicolon space then space straight S

  • is an empty set

  • contains exactly one element.

  • contains exactly two elements.

  • contains exactly two elements.

251 Views

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9.

A value of θ for which fraction numerator 2 space plus space 3 straight i space sin space straight theta over denominator 1 minus 2 straight i space sin space straight theta end fraction is purely imaginary is

  • π/3

  • π/6

  • sin to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 4 end fraction close parentheses
  • sin to the power of negative 1 end exponent open parentheses fraction numerator square root of 3 over denominator 4 end fraction close parentheses
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10.

If A = open square brackets table row cell 5 straight a end cell cell negative straight b end cell row 3 2 end table close square brackets and A adj A = AAT, then 5a +b is equal to

  • -1

  • 5

  • 4

  • 4


B.

5

Given, A =open square brackets table row cell 5 straight a end cell cell negative straight b end cell row 3 2 end table close square brackets and A adj A = AAT, Clearly, A (adj A) = |A|In|
space equals space open vertical bar table row cell 5 straight a end cell cell negative straight b end cell row 3 2 end table close vertical bar straight I subscript 2
space equals space left parenthesis 10 straight a space plus space 3 straight b right parenthesis straight I subscript 2 space equals space left parenthesis 10 straight a space plus space 3 straight b right parenthesis open square brackets table row 1 0 row 0 1 end table close square brackets
equals open square brackets table row cell 10 straight a plus 3 straight b end cell 0 row 0 cell 10 straight a plus 3 straight b end cell end table close square brackets space.... space left parenthesis straight i right parenthesis
and space AA to the power of straight T space equals space open square brackets table row cell 5 straight a end cell cell negative straight b end cell row 3 2 end table close square brackets open square brackets table row cell 5 straight a end cell 3 row cell negative straight b end cell 2 end table close square brackets
equals open square brackets table row cell 25 straight a squared plus straight b squared end cell cell 15 straight a minus 2 straight b end cell row cell 15 straight a minus 2 straight b end cell 13 end table close square brackets space... space left parenthesis ii right parenthesis
because space straight A space left parenthesis adj space straight A right parenthesis space equals space AA to the power of straight T
therefore space open square brackets table row cell 10 straight a plus 3 straight b end cell 0 row 0 cell 10 straight a plus 3 straight b end cell end table close square brackets space equals open square brackets table row cell 25 straight a squared plus straight b squared end cell cell 15 straight a minus 2 straight b end cell row cell 15 straight a minus 2 straight b end cell 13 end table close square brackets space
using space eqs space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
rightwards double arrow space 15 straight a minus space 2 straight b equals space 0 space
rightwards double arrow space fraction numerator 2 straight b over denominator 15 end fraction space space space.. left parenthesis iii right parenthesis
and space 10 space straight a space plus space 3 straight b space equals space 13
On space substituting space the space value space of space apostrophe straight a apostrophe space from space Eq. space left parenthesis iii right parenthesis space in space eq space left parenthesis iv right parenthesis comma space we space get
10. open parentheses fraction numerator 2 straight b over denominator 15 end fraction close parentheses plus 3 straight b space equals space 13
rightwards double arrow space fraction numerator 20 straight b space plus space 45 straight b over denominator 15 end fraction space equals space 13 space rightwards double arrow space fraction numerator 65 straight b over denominator 15 end fraction space equals space 13

Now, substituting the value of b in Eq. (iii) we get 
5a = 2
Hence, 5a + b = 2 +3 = 5

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